Pulse-level noisy quantum circuits with QuTiP

Boxi Li1, Shahnawaz Ahmed2, Sidhant Saraogi3, Neill Lambert4, Franco Nori4,5,6, Alexander Pitchford7, and Nathan Shammah8

1Peter Grünberg Institute - Quantum Control (PGI-8), Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
2Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
3Department of Computer Science, Georgetown University, 3700 O St NW, Washington, DC 20057, United States
4Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
5RIKEN Center for Quantum Computing (RQC), 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
6Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
7Department of Mathematics, Aberystwyth University, Penglais Campus, Aberystwyth, SY23 3BZ, Wales, United Kingdom
8Unitary Fund, Walnut, California 91789, USA

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The study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate-Scale Quantum (NISQ) computing. In this paper, we address the pulse-level simulation of noisy quantum circuits with the Quantum Toolbox in Python (QuTiP). We introduce new tools in $\texttt{qutip-qip}$, QuTiP's quantum information processing package. These tools simulate quantum circuits at the pulse level, leveraging QuTiP's quantum dynamics solvers and control optimization features. We show how quantum circuits can be compiled on simulated processors, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model, e.g., by simulating the Lindblad density-matrix dynamics or Monte Carlo quantum trajectories. In particular, the user can define environment-induced decoherence at the processor level and include noise simulation at the level of control pulses. We illustrate how the Deutsch-Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms. We also show how to easily reproduce experimental results on cross-talk noise in an ion-based processor, and how a Ramsey experiment can be modeled with Lindblad dynamics. Finally, we illustrate how to integrate these features with other software frameworks.

Quantum computation and quantum algorithms are deemed to be able to complete tasks that would be harder or impossible to achieve with classical resources. As an important tool, circuit simulation allows one to understand the possible advantages of quantum computation and develop new algorithms. In particular, the study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate-Scale Quantum (NISQ) computing. Many simulation tools have been developed to simulate quantum circuits at the level of unitary gates, in which noise is often added between perfect unitary gates through random Pauli noise or Kraus operators. In reality, however, the noise is much more complicated and varies from hardware to hardware.

To allow circuit simulation with noise models motivated by the physical model of the quantum hardware, we introduce new tools in qutip-qip, QuTiP's quantum information processing package to simulate quantum circuits at the pulse level. In our simulation framework, the quantum circuit is compiled for predefined hardware models, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model and simulated using QuTiP dynamic solvers. As an example, we illustrate how the Deutsch-Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms.

The tools we provide in this package simplify the simulation of noisy quantum circuits on different hardware models. Due to the modular design, it can be integrated with more hardware models, gate decomposition and optimization schemes. The pulse-level simulation could be helpful in quick verification of experimental results, developing quantum algorithms, such as variational quantum algorithms, and testing compiling and scheduling schemes with realistic noise models. Through hardware simulation and noise simulation, quantum error correction code and quantum mitigation protocols can also be studied, for example, simulating pulse-level and digital zero-noise extrapolation.

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